Geometric Construction: Finding the Correct Median in a Triangle

Look at triangle ABC below.

Which is the median?

αααAAABBBCCCDDDEEE

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1

Understand the problem

Look at triangle ABC below.

Which is the median?

αααAAABBBCCCDDDEEE

2

Step-by-step solution

To solve this problem, we must identify which line segment in triangle ABC is the median.

First, review the definition: a median in a triangle connects a vertex to the midpoint of the opposite side. Now, in triangle ABC:

  • Point A represents the vertex.
  • Point E lies on line segment AB.
  • Line segment EC needs to be checked to see if it connects vertex E to point C.

From the diagram, it appears that E is indeed the midpoint of side AB. Thus, line segment EC connects vertex C to this midpoint.

This fits the definition of a median, verifying that EC is the median line segment in triangle ABC.

Therefore, the solution to the problem is: EC \text{EC} .

3

Final Answer

EC

Practice Quiz

Test your knowledge with interactive questions

Fill in the blanks:

In an isosceles triangle, the angle between two ___ is called the "___ angle".

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